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Establishment of unified numerical methods for moving boundary problems

Research Project

Project/Area Number 23540150
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionMeiji University (2012-2013)
University of Miyazaki (2011)

Principal Investigator

YAZAKI Shigetoshi  明治大学, 理工学部, 准教授 (00323874)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords移動境界問題 / Hele-Shaw問題 / 曲率流方程式 / 曲率依存型接線速度 / 結晶成長 / スパイラル / 数値スキーム / 雪結晶 / 自由境界問題 / 画像処理 / Hele-Shaw流れ / 曲率流方程式(スロバキア,チェコ,金沢,福岡) / 移動境界問題(スロバキア,チェコ,金沢,福岡) / ヘレ・ショウ問題(チェコ,金沢,福岡) / 構造保存型スキーム(チェコ,金沢,福岡) / クリスタライン曲率流 / 曲率調整型スキーム / 保存型スキーム / 折れ線曲率流
Research Abstract

When the interface between different mediums moves, the interface is called moving boundary, and the problem of tracking moving boundaries mathematically and numerically is called moving boundary problem (MBP in short). In the present research, we have studied numerical methods for MBPs, and tried to develop quite general numerical schemes and establish unified numerical methods for various MBPs. Within the research periods, we could develop quite nice unified numerical methods for curvature flow equations which are typical MBPs. Mathematical proofs such as convergence of the numerical schemes are on-going research.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (19 results)

All 2014 2013 2012 2011 Other

All Journal Article (8 results) (of which Peer Reviewed: 2 results,  Open Access: 1 results) Presentation (9 results) (of which Invited: 3 results) Book (1 results) Remarks (1 results)

  • [Journal Article] A fast blow-up solution and degenerate pinching arising in an anisotropic crystalline motion2014

    • Author(s)
      T. Ishiwata and S. Yazaki
    • Journal Title

      Discrete Contin. Dynam. Systems

      Volume: A34, Issue5 Pages: 2069-2090

    • Related Report
      2013 Final Research Report
  • [Journal Article] On a gradient flow of plane curves minimizing the anisoperimetric ratio2013

    • Author(s)
      D. Sevcovic and S. Yazaki
    • Journal Title

      IAENG International Journal of Applied Mathematics

      Volume: 43(3) Pages: 160-171

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Journal Article] Polygonal Hele-Shaw problem with surface tension2013

    • Author(s)
      M. Kimura, D. Tagami and S. Yazaki
    • Journal Title

      Interfaces and Free Boundaries

      Volume: 15(1) Pages: 77-93

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Journal Article] A fast blow-up solution and degenerate pinching arising in an anisotropic crystalline motion2013

    • Author(s)
      T. Ishiwata and S. Yazaki
    • Journal Title

      Discrete Contin. Dynam. Systems A

      Volume: 34, Issue 5 Issue: 5 Pages: 2069-2090

    • DOI

      10.3934/dcds.2014.34.2069

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Computational and qualitative aspects of motion of plane curves with a curvature adjusted tangential velocity2012

    • Author(s)
      D. Sevcovic and S. Yazaki
    • Journal Title

      Mathematical Methods in the Applied Sciences

      Volume: 35(15) Pages: 1784-1798

    • Related Report
      2013 Final Research Report 2012 Research-status Report
  • [Journal Article] Evolution of plane curves with a curvature adjusted tangential velocity2011

    • Author(s)
      D. Sevcovic and S. Yazaki
    • Journal Title

      Jpn. J. Ind. Appl. Math

      Volume: 28(3) Pages: 413-442

    • NAID

      10030213835

    • Related Report
      2013 Final Research Report
  • [Journal Article] Computational studies of non-local anisotropic Allen-Cahn equation2011

    • Author(s)
      M. Benes, S. Yazaki and M. Kimura
    • Journal Title

      Mathematica Bohemica

      Volume: 136(4) Pages: 429-437

    • Related Report
      2013 Final Research Report
  • [Journal Article] Evolution of plane curves with a curvature adjusted tangential velocity2011

    • Author(s)
      Daniel Sevcovic and Shigetoshi Yazaki
    • Journal Title

      Japan J. Indust. Appl. Math.

      Volume: 28(3) Issue: 3 Pages: 413-442

    • DOI

      10.1007/s13160-011-0046-9

    • NAID

      10030213835

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] ある移動境界問題の構造を保存する数値解法について2013

    • Author(s)
      矢崎成俊
    • Organizer
      第22回東工大数理解析セミナー
    • Place of Presentation
      東京工業大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] On a structure-preserving numerical scheme for moving boundary problems2013

    • Author(s)
      S. Yazaki
    • Organizer
      Equadiff13
    • Place of Presentation
      Prague
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 離散移動境界問題2012

    • Author(s)
      矢崎成俊
    • Organizer
      研究集会「界面の数理と幾何解析」
    • Place of Presentation
      芝浦工業大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 移動境界問題に対する構造保存型スキームの構築に向けて2012

    • Author(s)
      矢崎成俊
    • Organizer
      神楽坂解析セミナー
    • Place of Presentation
      東京理科大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 方程式の〈うまい〉離散化を目指して2012

    • Author(s)
      矢崎成俊
    • Organizer
      NLPMサマーセミナー2012
    • Place of Presentation
      岬の宿 高砂
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 移動境界問題の離散化と離散版移動境界問題について2012

    • Author(s)
      矢崎成俊
    • Organizer
      第1回明治非線型数理セミナー
    • Place of Presentation
      明治大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 移動境界問題の離散化と離散版移動境界問題について2012

    • Author(s)
      矢崎成俊
    • Organizer
      語ろう数理解析
    • Place of Presentation
      芝浦工業大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Discretization of moving boundary problems and discretized moving boundary problems'2012

    • Author(s)
      Shigetoshi Yazaki
    • Organizer
      Algoritmy 2012
    • Place of Presentation
      Podbanske, Slovakia
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Moving boundaries with a curvature adjusted tangential velocity2011

    • Author(s)
      Shigetoshi Yazaki
    • Organizer
      The 4th Mathematical Society of Japan, Seasonal Institute (MSJ-SI)
    • Place of Presentation
      Kyushu University
    • Related Report
      2011 Research-status Report
  • [Book] 大学生のフーリエ解析2011

    • Author(s)
      矢崎成俊
    • Total Pages
      284
    • Publisher
      東京図書
    • Related Report
      2011 Research-status Report
  • [Remarks] Shigetoshi Yazaki

    • URL

      http://www.isc.meiji.ac.jp/~syazaki/index.html

    • Related Report
      2013 Annual Research Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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